Quadrupole ion trap mass spectrometers have been known for many years and were described by Paul and Steinwedel in U.S. Pat. No. 2,939,952. Ion traps are devices in which ions are introduced into or formed and contained within a trapping chamber formed by at least two electrode structures by means of substantially quadrupolar electrostatic fields generated by applying RF voltages, DC voltages or a combination thereof to the electrodes. To form a substantially quadrupole field, the electrode shapes have typically been hyperbolic.
Mass storage and analysis are generally achieved by operating the ion trap electrodes with values of RF voltage V, RF frequency f, DC voltage U, and device size r.sub.0 such that ions having their mass-to-charge ratios (m/e) within a finite range are stably trapped inside the device. The aforementioned parameters are sometimes referred to as trapping or scanning parameters and have a relationship to the m/e ratios of the trapped ions.
Quadrupole devices are dynamic. Instead of constant forces acting on ions, ion trajectories are defined by a set of time-dependent forces. As a result, an ion is subject to strong focusing in which the restoring force, which drives the ion back toward the center of the device, increases linearly as the ion deviates from the center. For two-dimensional ion trap mass spectrometers, the restoring force drives the ion back toward the center axis of the device.
The motion of ions in quadrupole fields is described mathematically by the solutions to a particular second-order linear differential equation called the Mathieu equation. Solutions are developed for the general ease, the two-dimensional case of the quadrupole mass filter, and the standard three-dimensional case of the quadrupole ion trap. Thus, in general, for any direction u where u represents x, y, or z, ##EQU1## where V=magnitude of radio frequency (RF) voltage
U=amplitude of applied direct current (d.c.) voltage PA0 e=charge on an ion PA0 m=mass of an ion PA0 r.sub.0 =device-dependent size PA0 .omega.=2.pi.f PA0 f=frequency of RF voltage PA0 K.sub.a =device-dependent constant for a.sub.u PA0 K.sub.q =device-dependent constant for q.sub.u PA0 k=integer where k={0, .+-.1, .+-.2, .+-.3, . . . } PA0 f=frequency of the RF component of the substantially quadrupole field PA0 f.sub.u =fundamental frequency for the secular motion of a given ion at q.sub.u eject along the u coordinate axis, and f.sub.u &lt;f.
Stability diagrams which represent a graphical illustration of the solutions of the Mathieu equation utilize a.sub.u as the ordinate and q.sub.u as the abscissa.
For a substantially quadrupole field defined by U, V, r.sub.0 and .omega. the locus of all possible m/e ratios maps onto the stability diagram as a single straight line running through the origin with a slope equal to -2U/V. This locus is also referred to as the scan operating line. For ion traps, the portion of the locus that maps within the stability region defines the range of ions that are trapped by the applied field.
FIG. 1 shows a stability diagram representative of the operation of a two-dimensional ion trap mass spectrometer. Knowledge of the diagram is important to the understanding of the operation of quadrupole ion trap mass spectrometers. The stable ion region is cross-hatched and shown bounded by .beta..sub.x and .beta..sub.z.
The ion masses that can be trapped depend on the numerical values of the trapping parameters U, V, r.sub.0 and .omega.. The relationship of the trapping parameters to the m/e ratio of the ions that are trapped is described in terms of the parameters "a" and "q" in FIG. 1. The type of trajectory a charged ion has in a quadrupole field depends on how the specific m/e ratio of the ion and the applied trapping parameters, U, V, r.sub.0 and .omega. combine to map onto the stability diagram. If these trapping parameters combine to map inside the stability envelope then the given ion has a stable trajectory in the defined field.
By properly choosing the magnitudes of U and V, the range of specific masses of trappable ions can be selected. If the ratio of U to V is chosen so that the locus of possible specific masses maps through an apex of the stability region, then only ions within a very narrow range of specific masses will have stable trajectories. However, if the ratio of U to V is chosen so that the locus of possible specific masses maps through the "middle" (a.sub.u =0) of the stability region, then ions of a broad range of specific masses will have stable trajectories.
Ions having a stable trajectory in a substantially quadrupole field are constrained to an orbit about the center of the field. Typically, the center of the field is substantially along the center of the trapping chamber. In essence, the stable ions converge toward the center of the quadrupole field where they form a "cloud" of ions constantly in motion about the center of the quadrupole field. Although the intensity of the quadrupole field decreases from locations near the electrode surface to the center of the quadrupole field, ion density (with respect to the ion occupied volume, not the volume of the trapping chamber) increases. Such ions can be thought of as being trapped by the quadrupole field. Hereinafter, ion occupied volume is defined as the smallest volume occupied by most of the trapped ions. Typically, 95% of the ions in the trapping chamber occupy this volume. The ion occupied volume is smaller than the trapping chamber.
If, for any ion m/e ratio, U, V, r.sub.0, and .omega. combine to map outside the stability envelope on the stability diagram, the given ion has an unstable trajectory in the defined field. Ions having unstable trajectories in a substantially quadrupole field attain displacements from the center of the field which approach infinity over time. Such ions can be thought of as escaping the field and are consequently considered untrappable.
For both two-dimensional and three-dimensional ion trap mass spectrometers, some performance criteria must be used to determine their quality as a point of reference. Five important performance criteria are signal-to-noise ratio, sensitivity, detection limit, resolution, and dynamic range. The design of any ion trap mass spectrometer must take these criteria into consideration. Additionally, negative effects due to space charge cannot be ignored.
A parameter that plays a significant role in the performance of ion trap mass spectrometers is the number of ions (N) trapped in the electrode structure. Under equivalent conditions, a greater number of ions (N) improves performance. The number of ions (N) is given by the relation: EQU N=.rho.v
where v is the ion occupied volume and .rho. is the average charge density. Since the charge density .rho. should be maintained as a constant to minimize the effects of space charge, only the ion occupied volume v can be increased to increase the total number of ions stored in the ion trap mass spectrometer. Merely increasing the volume of the trapping chamber in the radial direction (along the x- and/or z-axes) will not increase the ion occupied volume. The many embodiments of the present invention provide solutions to increasing the ion occupied volume v.
However, one limitation on increasing the trapping chamber radially (in a direction substantially parallel to the x-z plane) as opposed to axially (in a direction along the y-axis) is the restoring potential. For example, in a two-dimensional straight substantially quadrupole ion trap mass spectrometer, if the volume of the trapping chamber is increased arbitrarily in the radial direction (x and z directions), the restoring potential may not be suitable to contain the high m/e ions. To maintain the same restoring potential or achieve a suitable field, the power supply voltages must be increased, effectively defining the original substantially quadrupole field. But, as the embodiments of the present invention will show, if the volume of the trapping chamber is increased in the axial or non-radial direction (y direction) only, the power supply voltages need not be changed or increased. Thus, increasing the volume in the y direction increases the number of trapped ions, and improves the performance of the ion trap mass spectrometer.
Another limitation of increasing the volume of the trapping chamber in the radial direction is the mass range of ions trappable in the ion trap mass spectrometer. As the volume of the trapping chamber is increased radially, the trappable ion mass range decreases. This is because the maximum mass range is inversely proportional to the square of the device-dependent parameter r.sub.0 (that is, m.sub.max .alpha.1/r.sub.0.sup.2). Thus, as the volume of the trapping chamber is increased non-radially (in the y direction) only, r.sub.0 is not affected and thus, the same mass range of ions can be maintained.
For two-dimensional substantially quadrupole fields, no field exists in the y direction. So, from the general expression of .phi. for the substantially quadrupole field, ##EQU2## where .sigma.=0.
From Laplace's condition, EQU .lambda.+.gamma.=0
and so, EQU .lambda.=-.gamma.=1
As is well known in the art, the choice of 1 in the last equation is arbitrary. The substantially quadrupole field then becomes: ##EQU3## The two-dimensional substantially quadrupole fields can be generated by straight or curved electrodes. The most desirable surface of the rod-like electrodes is hyperbolic in shape.
The equation for the substantially quadrupole field for the three-dimensional ion trap can be derived by simply incorporating particle motion in the y direction. The simplest three-dimensional ion trap is defined by two end electrodes and a center ring electrode. The substantially quadrupole field within the ion trap exists in all three directions (x, y, z). As before, utilizing the general expression for the substantially quadrupole field and satisfying Laplace's condition, the potential .phi. at any point (x, y, z) is: ##EQU4##
Thus, for a particular applied potential .phi..sub.0 and device size r.sub.0, the potential .phi. may be obtained at any point (x, y, z). For greater device size r.sub.0, the same applied potential .phi..sub.0 will result in a smaller field .phi. at the same point (x, y, z). This, in effect, reduces the mass range of the ion trap mass spectrometer. As the device size r.sub.0 increases, the field at the same point (x, y, z) decreases and the restoring field will not be sufficient to drive the high m/e ions back toward the central axis. In order to have a sufficient restoring field, one must increase .phi..sub.0. Under some conditions, the limits on .phi..sub.0 may warrant replacing the power supplies to that which provide higher voltages. However, as the embodiments of the present invention will show, increasing the volume of the trapping chamber by increasing the dimensions in the y-direction only and effectively creating an ellipse-shaped electrode structure also enlarges the ion occupied volume.
Space charge is the perturbation in an electrostatic field due to the presence of an ion or ions. This perturbation forces the ion to follow trajectories not predicted by the applied field. If the perturbation is great, the ion may be lost and/or the mass spectral quality may degrade. Spectral degradation refers to broad peaks giving lower resolution (m/.DELTA.m), a loss of peak height reducing the signal-to-noise ratio, and/or a change in the measured relative ion abundances. Space charge thus limits the number of ions one can store while still maintaining useful resolution and detection limits.
The novel ion trap mass spectrometers disclosed herein are used with a number of mass analysis methods. One embodiment of this method, the mass selective instability scan, is described in U.S. Pat. No. 4,540,884, which is incorporated herein by reference. In this method, a wide mass range of ions of interest is created and stored in the ion trap during an ionization step. The RF voltage applied to the ring electrode of the substantially quadrupole ion trap is then increased and trapped ions of increasing specific masses become unstable and either exit the ion trap or collide on the electrodes. The ions that exit the ion trap can be detected to provide an output signal indicative of the m/e (mass to charge ratio) of the stored ions and the number of ions.
An enhanced form of the mass selective instability scan incorporates resonance ejection. Refer to U.S. Pat. Nos. 4,736,101 and Re. 34,000. They demonstrate that introducing a supplemental AC field in the ion trap mass spectrometer facilitates the separation and ejection of adjacent m/e ions. The frequency f.sub.res of the supplemental AC source determines the q.sub.u at which ions will be ejected. If the frequency f.sub.res of the supplemental AC field matches a secular component frequency of motion of one of the m/e ion species in the ion occupied volume, the supplemental field causes those specific ions (e.g., those ions at the specific q) to oscillate with increased amplitude. The magnitude of the supplemental field determines the rate of increase of the ion oscillation. Small magnitudes of the supplemental field will resonantly excite ions, but they will remain within the substantially quadrupole field. Large magnitudes of the supplemental field will cause those ions with the selected resonant frequency to be ejected from or onto the trapping chamber. In some commercial ion traps, a value of 2 to 10 volts peak-to-peak measured differentially between the two end caps have been used to resonantly eject ions.
The frequency of the supplemental AC field f.sub.res is selected such that the ions of specific m/e ratios can develop trajectories that will make the ion leave the ion occupied volume. The resonant frequency f.sub.res =kf.+-.f.sub.u where,
The expression for f.sub.res represents the frequency components of the solutions of the exact equations of ion motion in a harmonic RF potential. Typically, k=0 so that f.sub.res =f.sub.u and smaller applied AC amplitude potentials are required; however, any frequency satisfying the general expression for f.sub.res and of sufficient amplitude will cause ions to leave the trapping chamber.
A supplemental field can also be used with the MS/MS method, described in U.S. Pat. Nos. 4,736,101 and Re. 34,000, which are incorporated herein by reference. Essentially, MS/MS involves the use of at least two distinct mass analysis steps. First, a desired m/e is isolated (typically with a mass window of .+-.0.5 amu). Ejection of undesired ions during the isolation step is accomplished by, and not limited to, several techniques: (i) applying DC to the ring, (ii) applying waveforms, and (iii) scanning the RF so that undesirable ions pass through and are ejected by a resonance frequency. This is MS.sup.1. After undesired ions are ejected, the RF (and possibly DC) voltage is lowered to readjust the m/e range of interest to include lower m/e ions. Fragments, or product ions can then be formed when a neutral gas, such as helium, argon, or xenon, is introduced in the ion trapping chamber in combination with a resonance excitation potential applied to the end caps. These fragments remain in the ion trapping chamber. In the second mass analysis step, the mass selective instability scan is used, with or without resonance ejection, to eject the fragment ions into a detector. This is MS.sup.2. Thus, at least two mass spectrometry steps were performed in one device. Repetitive tandem MS techniques (i.e. (MS).sup.n) may also be employed for n distinct mass spectrometry steps.
The MS.sup.2 step can be accomplished as follows: A supplemental AC field is applied after the primary RF field is decreased at the end of the first scan and prior to the second scan to eject undesired ions of a specific m/e ratio. Upon ejection, the supplemental AC field is turned off and the primary RF field is increased to eject desired ions into a detector. Variations of this technique, as disclosed in U.S. Pat. Nos. 4,736,101 and Re. 34,000, can be utilized. Thus, manipulation of the RF amplitude, RF frequency, supplemental AC field amplitude, supplemental AC field frequency, or a combination thereof promotes ejection of ions for detection after the formation and trapping of product ions. For example, the supplemental AC field can be turned on during the second scan of the primary RF field. Alternatively, instead of a second scan period, the RF field is kept constant while the frequency of the supplemental AC field is varied. Ejection can also be achieved by changing the magnitude of the supplemental AC field while changing the amplitude of the RF component of the substantially quadrupole field.
Several people have trapped ions in a two-dimensional RF-quadrupole. Beaugrand, Devant, Mestdagh, Jaouen, and Rolando trapped and stored ions in a RF-quadrupole and showed the trapping efficiency to be quite high. C. Beaugrand, G. Devant, H. Mestdagh, D. Jaouen, and C. Rolando, 5 Spectroscopy Int. J. 265 (1987). The trapping of ions in a substantially quadrupole field is further discussed in U.S. Pat. No. 4,755,670 where a Fourier transform method of analysis is taught by Syka and Fies. Dolnikowski, Kristo, Enke, and Watson have also trapped ions in a RF-quadrupole where they studied ion/molecule reactions. G. G. Dolnikowski, M. J. Kristo, C. G. Enke and J. T. Watson, 82 Int. J. of Mass Spectrom. and Ion Proc. 1 (1988). After the ion molecule reactions occurred in the storage cell, these ions were pulsed into a quadrupole mass filter for mass analysis. Beaugrand and co-workers also studied the chemical equilibrium and kinetic and thermodynamic parameters of select ion/molecule reactions. C. Beaugrand, D. Jaouen, H. Mestdagh, and C. Rolando, 61 Anal. Chem. 1447 (1989). This instrument consisted of three quadrupoles where the central quadrupole served as a storage and reaction cell. In all of these cases the ions were never scanned out of the quadrupole using the mass selective instability scan mode.
Curved ion traps have also been explored. In 1969 Church described a ring ion trap and a "racetrack" ion trap geometry. The ring ion trap was formed by bending the more typical two-dimensional quadrupole rod electrodes into a circle. D.A. Church, 40 Journal of Applied Physics 3127 (1969). Church worked at a high fundamental frequency, 52 Mhz, a small r.sub.0 =0.16 cm (distance from the center of the field to the edge of a quadrupole rod), and R=7.2 cm (radius of the ring structure). This made R/r.sub.0 =45 which is relatively large. The large R/r.sub.0 allowed the field formed in this circular ion trap to more closely mimic an ideal two-dimensional substantially quadrupole field. That is, by minimizing the effects of the induced multipole fields the non-two-dimensional resonances are reduced and trapping time is maximized. Church was able to trap and measure the presence of H.sup.+ (m/e=1), .sub.3 He.sup.+ (m/e=3), and noted that "heavier ions" Hg.sup.+ (m/e=200.6) and Hg.sup. +2 (m/e=100.3) could also be trapped as described by G. R. Hugget and S. C. Menasian. The detection of ions in Church's work was accomplished using a resonance absorption technique. No helium damping gas was added to their device.
U.S. Pat. No. 3,555,273 (issued to James T. Arnold) describes a three-dimensional quadrupole structure. However, the structure described and claimed is a mass filter.
Other ion traps with six-electrode structures have been studied. These six-electrode ion traps have been described with flat plats and annular rings, but using hyperbolic electrodes is preferred. These structures could be scanned using the mass selective instability scan mode as in the three-electrode counterpart or the straight two-dimensional quadrupole as stated here.
Applicant is not aware of any prior art that attempts to improve the performance of ion trap mass spectrometers in the manner herein disclosed. The geometries with an elongated trapping chamber forming the enlarged ion occupied volume and the particular detection scheme have not been used with the mass-selective instability scan mode with or without resonance excitation ejection waveform.